Assessing concentration and diversification in portfolio credit risk models

This thesis explores existing and proposes new methods for assessing concentration risk in default-only credit risk models. Within the existing methods, the analytic Granularity Adjustment is studied in the single factor Gaussian threshold and in the CreditRisk+ framework. These adjustments are tested on a sample portfolio in the presence of recovery risk, and we show that the CreditRisk+ adjustment is more conservative than the Gaussian threshold adjustment. Furthermore, we show that in the presence of recovery risk, the accuracy of the adjustment on exposure level deteriorates. Additionally, the Granularity Adjustment is extended to an independent single factor \textit{t}-threshold model to account for heavier tailed asset returns. Based on the independent single factor \textit{t}-threshold model, we suggest an ASRF equivalent that could serve as an alternative to the current IRB framework. Although much existing literature is focusing on developing analytical methods for measuring concentration risk, recent advances in computational speed make Monte Carlo methods an interesting substitute for measuring concentration risk. To this extend, we propose a split between Monte Carlo based Economic and Regulatory Concentration Risk and show that these measures do not coincide for a given portfolio. This method involves a novel way of assessing idiosyncratic risk in multi factor frameworks. In order to assess sector concentration risk, this thesis proposes a Diversification Factor and a Capital Diversification Index as risk management tools. Finally, this thesis provides a clear account of the effects of concentration, diversification and recovery risk on the portfolio loss distribution for both Gaussian and \textit{t}-threshold models. This thesis was carried out in close cooperation with ING Bank.Applied Mathematics | Financial Engineerin